Not Even Wrong

It’s been unusually long since my last posting, with the main reasons being that

Garrett Lisi has a new paper on the arXiv, with the rather over-the-top title of An Exceptionally Simple Theory of Everything. Sabine Hossenfelder has a typically excellent posting about the paper, and Garrett has been discussing his work with people in the comment section there. Lubos Motl, has a typically, how shall I say, Lubosian posting on the topic.

I’m the first person thanked in the acknowledgment section of the paper, but at Sabine’s blog Garrett explains that this is just because he is using reverse alphabetical order. I’ve corresponded with him in the past about his research in this area, without being able to provide any real help other than a certain amount of encouragement. Two of the ideas he is pursuing are general ones I’m also very fond of. One is well-known, and many people have also tried this, it’s the idea of bringing together the internal gauge symmetry and the symmetry of local frame rotations. The problems with this are also well-known, and some have been brought up by the commenters at Sabine’s blog. I don’t think Garrett has found the answer to this, or that he claims to. I’m still hopeful that this line of thinking will lead somewhere, but think some dramatically different new idea about this is still needed. The other idea he likes is that of trying to interpret the fermionic degrees of freedom of the BRST method for handling gauge invariance as providing the fermions of the Standard Model. I suspect there is something to this, but to get anywhere with it, a much deeper understanding of BRST will be required. I’ve been spending a lot of time trying to understand some of the mathematics related to BRST in recent years, and am in the middle of writing some of this up. It seems to me that there is a lot that is not understood yet about this topic even in much simpler lower-dimensional contexts, so we’re a long way from being able to really see whether something can be done with this idea in a realistic four-dimensional setting.

One idea Garrett is fond of that has generally left me cold is the idea of unification via a large simple Lie algebra like E₈. While there may be some sort of ultimate truth to this, the problem is that, just as for GUTs and for superstring models, all you’re doing when you do this is changing the unification problem into the problem of what breaks the large symmetry. This change in the problem adds some new structure to it, but just doesn’t seem to help very much, with the bottom line being that you get few if any testable predictions out of it (one exception is with the simplest GUTs, where you do get a prediction, proton decay, which turns out to be wrong, falsifying the models).

Anyway, I’m glad to see someone pursuing these ideas, even if they haven’t come up with solutions to the underlying problems. Garrett is a serious and competent researcher who has pursued a non-traditional career path, and was recently awarded a grant to by the FQXI organization. You can read more about him in an article on their web-site.

Unfortunately, some of the reaction to Garrett’s article has been depressing. A commenter who sounds well-informed but hides behind anonymity goes on about “this nonsense” (although Garrett’s polite reaction to him/her did lead to a more sensible discussion). Early on in my experience with blogs I believed that no serious professional in particle physics would attack someone and try and carry on a scientific argument anonymously, so any such comments had to be coming from misguided students, or someone not in the profession. Unfortunately I’ve all too often seen evidence that I was wrong about this. Lubos Motl on his blog denounced the fact that Garrett’s paper appeared in the hep-th section of the arXiv, then later wrote in to Sabine’s blog to crow that it had been removed from hep-th. As always with the arXiv, how moderation occurs there is non-transparent, so I don’t know how or why this happened. My own experience with the arXiv over trackbacks to hep-th has been a highly disturbing one. The current hep-th policy seems to be to allow any sort of nonsense to be posted there if it fits into the current string-theory-based ideology (see for example here), while suppressing any criticism of this. A paranoid person might be tempted to wonder whether hep-th is being moderated by someone so ideological and petty that criticism of string theory or including string theory critics in an acknowledgment section would be cause for having ones article removed from hep-th…

Update: I hear from Garrett that the story of this paper at the arXiv is that it was submitted to gr-qc, not hep-th. Before it was posted, it was re-classified as hep-th, and appeared there. Later on (after the appearance of Lubos’s blog entry denouncing the arXiv for allowing the paper on hep-th I believe), it was re-classified again, this time as general physics (with cross-listing to hep-th).

Update: Latest news about this is that the paper has now been reclassified again, to the perfectly appropriate hep-th, cross-listed as gr-qc, although no one seems to know why this happened. Another continuing mystery is the trackback situation: there are four trackbacks to the paper, to postings by Lubos, Bee, and to Physics Forums, as well as to an old TWF from John Baez that doesn’t even link to the paper. My postings still seem to be non-trackback worthy on hep-th, not that I can argue with this particular case, since the discussion elsewhere has been more substantive (except for Lubos’s, which is valuable for the way it accurately represents the hysterical reaction to speculation that is not string theory speculation all too common in certain quarters).

Update: Garrett is making the news here. Whether this is a good thing is yet another question for debate on the next thread, I guess. A lot of the attraction for the media seems to be his personal story. Maybe it’s a good thing for physics for people to see that one can be a theoretical physicist while surfing in Hawaii…

Update: Lisi-mania spreads. See stories in New Scientist, the Ottawa Citizen, Slashdot, and probably lots of other places I haven’t noticed.

Update: Steinn Sigurdsson has an excellent posting summarizing the situation. As usual, blogs are the place to get the highest quality information about scientific issues…

Update: I’ve given up on keeping track of the media stories on this. For some discussion of the representation theory involved, see this posting by Jacques Distler, and comments from Garrett.

Update: The Angry Physicist examines the Distler critique in some detail.

The past two days I’ve been at a conference here in Lisbon organized by the Gulbenkian Foundation on the ostensible topic of Is Science Near Its Limits? The Gulbenkian is probably the most well-known and best-funded cultural organization in Portugal, and it includes a world-famous museum housing the wonderful art collection of its founder, Calouste Gulbenkian, who made his fortune in the oil business early during the last century.

The conference was extremely well-run and well-attended, filling a large lecture hall where there was simultaneous translation of the talks into Portuguese. It was organized by literary critic, writer and polymath George Steiner, who gave the introductory talk. I hadn’t known that Steiner had originally started out studying mathematics, but was discouraged from pursuing a career in the subject at the University of Chicago by Irving Kaplansky, which led to his turning to the study of literature and philosophy. Steiner had quite a lot to say provocative to scientists, including questioning whether they had been able to justify to the public the large sums of money being spent on the LHC, and characterizing the lack of testability of string theory as strong evidence that science had hit a limit beyond which it could not progress.

On the whole the rest of the speakers actually didn’t have much to say about limits of science, taking the standard view of most scientists that their own field had a bright future, with no limits in sight. The final talk of the conference did return to the limits issue, with John Horgan giving an uncompromising defense of the thesis of his 1996 book The End of Science (although he did allow that possible advances in neuroscience such as the decoding of a neural code, could be as revolutionary as previous advances). While the scientists in the audience took Steiner’s attacks in stride, partly because he was our host, they were less charmed by Horgan, who got a rather hostile reaction from many of them. I hope he’ll write about his point of view on the conference at his blog, or discuss it in one of his Bloggingheads discussions with George Johnson.

I was one of the few other speakers discussing the question of limits, with my talk emphasizing that particle physics is now in a new, different environment than that of the past, one in which progress, even revolutionary progress, is possible, but much more difficult. A written version of my talk is available here. I was paired with string theorist Dieter Lust, who gave a presentation of the case for string theory unification and the Landscape. We were introduced by Gustavo Calstelo Branco of the IST, who emphasized recent advances in our understanding of neutrinos. Also speaking in another session was Luis Alvarez-Gaume of CERN, who gave a very upbeat talk on the prospects for particle physics, taking the point of view on string theory that, like any idea, string theorists will give up on it if it doesn’t work out. He already sees a diminishment of interest in string theory among particle physicists, with people moving instead towards subjects that promise some sort of interaction with experimental data. The three of us were brought together later for an interesting small and very lively discussion of the issues surrounding string theory and recent media attention to it. This was taped, and may appear in some form or other in the future.

Update: There’s an entertaining conversation between John Horgan and George Johnson about the Lisbon conference now up at Bloggingheads.

Robert Shrock of Stony Brook sent me the following to post as a response to one of the comments on the latest posting. With his permission I’m putting it here as a separate posting, since I think it’s a valuable informed summary of the current state of technicolor/extended technicolor models.

I would like to respond to Eric’s recent comment on Oct. 23 in which he said that “technicolor models were..eventually rejected due to some serious shortcomings. Namely, in order to generate fermion mass hierarchies for the SM fermions, one ends up with serious problems with FCNC’s.” and that these theories “led to a plethora of technimesons, for which there is absolutely no evidence.”.

While it is true that FCNC’s are a relevant constraint on technicolor and extended technicolor (TC/ETC) theories and were viewed as very serious before the development of walking TC in the mid-1980’s, they do not obviously exclude TC/ETC models where the TC sector has walking behavior. The walking (slow running of the TC gauge coupling over an extended range), results naturally from the presence of an approximate IR fixed point in the renormalization group equation for the TC gauge coupling. This walking has the effect of enhancing SM fermion masses for a fixed set of ETC breaking scales. Indeed, since the mid-1980’s, the only viable TC models have been those with walking behavior. This walking allows one to use higher ETC breaking scales and still obtain the same SM fermion masses. It also enhances the masses of (pseudo)Nambu-Goldstone bosons. This was discussed in T. Appelquist and L. C. R. Wijewardhana, Phys. Rev. D 35, 774 (1987); Phys. Rev. D36, 568 (1987) and reviewed already a number of years ago, e.g., in R. S. Chivukula, hep-ph/9503202, hep-ph/9803219 and K. Lane, hep-ph/0202255, as well as more recent reviews such as C. Hill and E. Simmons, hep-ph/0203079 (published in Phys. Repts.) and my brief SCGT06 review, hep-ph/0703050. PNGB’s in one-family TC/ETC models may still be a phenomenological concern, but the early estimates of their masses were substantially increased by walking TC.

Let me explain in more detail how TC/ETC models may be able to satisfy FCNC constraints. ETC models generically gauge the generational index and combine it with TC, so a simple SU(N_ETC) model has N_ETC=N_gen+N_TC. With three generations of SM fermions, N_gen=3 and using the minimal value of N_TC, namely N_TC=2, this yields an SU(5) ETC theory. The SU(5) ETC symmetry can break to an exact residual vectorial SU(2) TC gauge group in three stages, characterized by three different mass scales, $\Lambda_j$, j=1,2,3. The ETC gauge bosons with masses $\Lambda_1$ mediate transitions between SM fermions of the first generation and the technifermions, and so forth for the other scales. With the values
$$\Lambda_1 \simeq 10^3\ TeV$$
$$\Lambda_2 \simeq 10^2\ TeV$$
and
$$\Lambda_3 \simeq few\ TeV$$
this model appears to be able to fit constraints on FCNC processes. Consider, for example, one of the most severe such constraints, arising from $K^0 – \bar K^0$ mixing. In early studies in the 1980’s, in the absence of an explcit ultraviolet ETC completion, one simply wrote down a generic form for the low-energy effective Lagrangian for this process, $\simeq (c/\Lambda_{ETC}^2)$ times the relevant four-quark operators, where $\Lambda_{ETC}$ was taken to be “the” ETC breaking scale. But the key observation is the following: in the initial $\bar K^0$, the d sbar pair can annhilate to produce a $V^2_1$ ETC gauge boson, where the indices are the gauged generational indices. But this cannot directly produce the s dbar pair of the K⁰, which requires a $V^1_2$ ETC gauge boson. Hence, in order for the K-Kbar transition to proceed, the the actual ETC propagator factor is not 1 over the mass squared of the $V^2_1$ gauge boson, $1/\Lambda_1^2$, but instead
$$(1/\Lambda_1^2)\ \Pi\ (1/\Lambda_1^2)$$
where Π denotes the requisite nondiagonal propagator insertion that takes a $V^2_1$ to a $V^1_2$. Using a reasonably ultraviolet-complete ETC theory, in the paper hep-ph/0308061, published as Phys. Rev. D 69, 015002 (2003), Appelquist, Piai, and I showed, via explicit calculation of the ETC gauge boson mixings, that the nondiagonal ETC gauge boson mixing term is generically of order the square of a low ETC breaking scale, essentially as a consequence of a residual approximate generational symmetry in the ETC theory. This suppresses the $K^0 -\bar K^0$ mixing strongly, by a factor like $(\Lambda_3/\Lambda_1)^2$, i.e., the coefficient of the four-quark operator is not $1/\Lambda_1^2$ but the much smaller $\Lambda_3^2/\Lambda_1^4$, which is sufficient to satisfy the constraint from the experimentally measured mixing and resultant $K_L – K_S$ mass difference. In this and a series of other papers, taking account of the mixing between ETC group eigenstates of fermions to form mass eigenstates, we also examined many other FCNC constraints on TC/ETC theories and showed that they appear to be able to be satisfied.

There are also FCNC processes that do not involve mixing of ETC gauge bosons. For example, the (conjugate of the) process $s \rightarrow d\ \mu^-\ e^+$ via exchange of a virtual $V^2_1$ ETC gauge boson gives rise to $K^+ \rightarrow \pi^+\ \mu^+ e^-$, for which the upper bound on the branching ratio (from the E865 experiment at BNL) is $BR(K^+ \rightarrow \pi^+\ \mu^+\ e^-) < 1.3 \times 10^{-11}$ (90 % CL). This is satisfied with the above value, $\Lambda_1 = 10^3\ TeV$.

Although Eric did not mention the effect that technifermions have on Z and W boson propagators, these also serve as a stringent constraint on technicolor models, especially the electroweak S parameter. However, because technicolor is strongly interacting at the scale of a few hundred GeV, it is not possible to use a perturbative estimate of S, and nonperturbative estimates based, e.g., on spectral function integrals, are difficult to make reliably for a walking TC theory since one cannot just scale up results from QCD. (There have been a number of papers over the years giving estimates on this, and I can send a list to anyone who is interested, but the issue is not resolved yet.)

In the SM, the electroweak symmetry breaking (EWSB) is produced by the vacuum expectation value of the hypothesized Higgs field. But this breaking is simply put in by hand, via an ad hoc choice of a negative coefficient for the quadratic Higgs term. No explanation is given in the SM of why this coefficient was not positive, when, a priori, it could just as well have been. Since the SM give no explanation for this negative sign of the coefficient, it does not provide a satisfactory fundamental explanation for EWSB. Indeed, it is interesting to recall that in both of the previous two main cases where a scalar field was used in phenomenological models for spontaneous symmetry breaking, namely in the Ginzburg-Landau free energy functional for superconductivity and the Gell-Man Levy sigma model for chiral symmetry breaking in hadronic physics, the microscopic physics did not involve the vacuum expectation value of a fundamental scalar field, but instead a bilinear fermion condensate – the Cooper pair in the BCS theory and the quark condensate in the case of QCD. In technicolor theories, it is precisely this type of bilinear fermion condensate – now involving technifermons,- which is responsible for electroweak symmetry breaking. Furthermore, the quark condensate in QCD already breaks electroweak symmetry. Thus, the original construction of technicolor models by Weinberg and Susskind was quite well motivated.

This is, of course, not to say that TC/ETC theories do not face many challenges. They are very ambitious, since they try to explain both EWSB and the spectrum of SM fermion masses, and no fully realistic model of this type has been constructed. Moreover, it is certainly true that far more people are currently working on various variants of SUSY models than on dynamical EWSB approaches such as TC/ETC. But at least readers should know that Eric’s comment refers to the old TC theories of the early 1980’s, which were, indeed, rejected; the results of more recent work indicate that modern walking TC theories appear to be able to satisfy FCNC constraints. PNGB’s and the S parameter are concerns, but, in the opinion of a number of us who work in this area, they do not obviously exclude these theories. In any case, we should know soon from the LHC whether dynamical EWSB via TC/ETC or some other possibility like low-energy SUSY is realized in nature.

I haven’t been able to confirm Lubos Motl’s claims that the Perimeter Institute offered him a job, but yesterday they announced that Lenny Susskind has accepted an offer to join them as an associate member. According to the announcement, this means that “he will spend focused time at PI each year to conduct research activities.”

At the Frankfurt book fair, Backreaction’s Stefan Scherer took a picture of one of the displays, that featured a large poster advertising Susskind’s forthcoming book The Black Hole War, which carries the subtitle “My battle with Stephen Hawking to make the world safe for quantum mechanics”.

Update: Marcus at Physicsforums points to this interview with Susskind about his forthcoming book:

For two decades an intellectual war took place between Stephen Hawking, on the one side, and myself and Gerard ‘t Hooft on the other. The book is about the scientific revolution that the controversy spawned, but also about the colorful personalities and the passions that gave the story its drama. The story starts in Werner Ehrhardt’s Mansion in San Francisco, and eventually passes through all seven continents, including Antarctica.

Various things that I’ve been wanting to mention:

Steven Hawking has a paper out, on his version of the Landscape story, using amplitudes that don’t rely upon string theory or eternal inflation. But just like the string theory Landscape I don’t see how his proposal is testable. It completely gives up on saying anything about particle physics, even statistically

If the volume weighted amplitude for the standard model vacuum is non-zero, it is irrelevant what the volume weighted amplitudes for other vacuum states are. The theory can not predict a unique vacuum state. Instead we have to input that we live in the standard model vacuum.

He ends with

The amplitudes will be highest for states in which the whole universe is in a single state, rather than a mosaic of different states, as predicted by eternal inflation. There will be no primordial production of topological defects, such as monopoles, and cosmic strings. Not all states in the landscape will have significant amplitudes, but there will be more than one that do, so M theory does not predict a unique low energy particle physics theory. It is implausible that life is possible only in one of these states, so we might have chosen a better location.

John Baez has a new This Week’s Finds out, with interesting discussions of the topos-theoretic approach to quantum theory, and the analogy between the integers and three-dimensional space. This semester he is running a seminar on “Geometric Representation Theory” (not clear how close this is to the use of the term by those representation theorists who work with D-modules). Videos and lecture notes from the talks are available, along with some blog postings (see here and here).

As always, Terry Tao’s blog has wonderful postings and articles, often of a general expository nature. For some recent examples, see one about the Schrodinger Equation, and another about Jordan normal form.

Besides excellent expository physics postings such as the recent one on single top production, Tommaso Dorigo gives a more realistic view of the academic life than most other blogs. For some understanding of how academics feel about the travel opportunities that conferences present, and what they think about the question of whether their employer should be financing what sometimes feels like a vacation, see his recent posting on Ethical aspects of professional conference-going. I strongly endorse his recommendation of the David Lodge novel Small World.

There’s a string theory wiki out there, aimed at students trying to learn string theory, which has been set up by the Centre for Research in String Theory at Queen Mary College. Much of the site is a listing of the one thousand or so review and other papers an aspiring young theorist should read and absorb to get an idea of what is going on with string theory. Also listed are various blogs, including this one, that might save students some of this reading…